Journal of Low Temperature Physics

, Volume 177, Issue 3–4, pp 193–201 | Cite as

Multi-vortex State Induced by Proximity Effects in a Small Superconducting Square

  • J. Barba-Ortega
  • J. D. González
  • Edson Sardella


The influence of the different negative values of the deGennes parameter \(b\) in the thermodynamic properties of a superconducting infinitely long prism of square cross section area \(S=9\xi ^{2}(0)\) in the presence of a magnetic field is investigated theoretically by solving numerically the nonlinear Ginzburg-Landau equations; \(\xi (0)\) is the coherent length at zero temperature. We obtain the vorticity, magnetic induction, Cooper pair density, magnetization and phase of the order parameter as functions of the external applied magnetic field and the \(b\) parameter. Our results show that a multi-vortex state appear in the sample choosing a convenient value of \(b<0\) parameter, even for such small system. Also, we study a superconducting parallelepiped of volume \(V=Sd\) by means of true \(3D\) numerical simulations; \(d\) is the height of the parallelepiped. We focused our analysis on the way which the magnetization curves approximate from \(d\) finite to the characteristic curve of \(d\rightarrow \infty \). This is the case for which the magnetic field and the order parameter are invariant along \(z\)-direction. For a superconductor of size \(S=9\xi ^2(0)\) we find that the limit below which the system should be considered a real three-dimensional sample when is \(d=8\xi \).


Ginzburg-Landau deGennes parameter Small mesoscopics 



ES thanks the Brazil Agency FAPESP for financial support. This work was partially financed by the Universidad del Magdalena (Fonciencias) and the Colombian Agency COLCIENCIAS through doctoral scholarships 567.


  1. 1.
    V.L. Ginzburg, L.D. Landau, Zh. Eksp. i Teoret. Fiz. 20, 1064 (1950)Google Scholar
  2. 2.
    W.P. Halperin, Rev. Mod. Phys. 58, 533 (1986)CrossRefADSGoogle Scholar
  3. 3.
    Y.G. Sun, Y.N. Xia, Science. 298, 2176 (2002)CrossRefADSGoogle Scholar
  4. 4.
    D.J. Harrison, K. Fluri, K. Seiler, Z.H. Fan, C.S. Effenhauser, A. Manz, Science. 261, 895 (1993)CrossRefADSGoogle Scholar
  5. 5.
    D.S. Golubovic, M.V. Milosevic, F.M. Peeters, V.V. Moshchalkov, Phys. Rev. B. 71, 180502 (2005)Google Scholar
  6. 6.
    A.E. Koshelev, V.M. Vinoku, Phys. Rev. B. 64, 134518 (2001)CrossRefADSGoogle Scholar
  7. 7.
    D.S. Golubovic, M.V. Milosevic, F.M. Peeters, V.V. Moshchalkov, Phys. Rev. B. 71, 180502 (2005)CrossRefADSGoogle Scholar
  8. 8.
    M.V. Milosevic, F.M. Peeters, Phys. Rev. Lett. 93, 267006 (2004)CrossRefADSGoogle Scholar
  9. 9.
    M.V. Milosevic, F.M. Peeters, Phys. Rev. B. 68, 024509 (2003)CrossRefADSGoogle Scholar
  10. 10.
    G.R. Berdiyorov, B.J. Baelus, M.V. Milosevic, F.M. Peeters, Phys. Rev. B. 68, 174521 (2003)CrossRefADSGoogle Scholar
  11. 11.
    M.V. Milosevic, G.R. Berdiyorov, F.M. Peeters, Appl. Phys. Lett. 91, 212501 (2007)CrossRefADSGoogle Scholar
  12. 12.
    J.K. Gregory, M.S. James, S.J. Bending, C.J. van der Beek, M. Konczykowski, Phys. Rev. B. 64, 134517 (2001)CrossRefADSGoogle Scholar
  13. 13.
    Y. AĠenenko, H. Rau, S.V. Yampolskii, J. Phys. 17, L93 (2005)Google Scholar
  14. 14.
    R.G. Mints, I.B. Snapiro, Phys. Rev. B. 47, 3273 (1993)CrossRefADSGoogle Scholar
  15. 15.
    E. Zeldov, A.I. Larkin, V.B. Geshkenbein, M. Konczykowski, D. Majer, B. Khaykovich, V.M. Vinokur, H. Shtrikman, Phys. Rev. Lett. 73, 1428 (1994)CrossRefADSGoogle Scholar
  16. 16.
    J. Barba-Ortega, J.D. Gonzalez, E. Sardella, J. Low. Temp. Phys. 174, 96 (2014)CrossRefADSGoogle Scholar
  17. 17.
    J. Barba-Ortega, E. Sardella, J.A. Aguiar, Supercond. Sci. Technol. 24, 015001 (2011)CrossRefADSGoogle Scholar
  18. 18.
    P.N. Lisboa Filho, A.L. Malvezzi, E. Sardella, Physica B. 403, 1494 (2008)CrossRefADSGoogle Scholar
  19. 19.
    J. Barba-Ortega, J.A. Aguiar, Physica C. 469, 754 (2009)CrossRefADSGoogle Scholar
  20. 20.
    B.J. Baelus, S.V. Yampolskii, F.M. Peeters, Phys. Rev. B. 65, 024510 (2001)CrossRefADSGoogle Scholar
  21. 21.
    W.D. Gropp, H.G. Kaper, G.K. Leaf, D.M. Levine, M. Palumbo, V.M. Vinokur, J. Comput. Phys. 123, 254 (1996)MathSciNetCrossRefMATHADSGoogle Scholar
  22. 22.
    F. Rogeri, R. Zadorosny, P.N. Lisboa-Filho, E. Sardella, W.A. Ortiz, Supercond. Sci. Technol. 26, 075005 (2013)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • J. Barba-Ortega
    • 1
  • J. D. González
    • 2
  • Edson Sardella
    • 3
    • 4
  1. 1.Departamento de FísicaUniversidad Nacional de ColombiaBogotáColombia
  2. 2.Grupo de Teoría de la Materia CondensadaUniversidad del MagdalenaSanta MartaColombia
  3. 3.Departamento de FísicaUNESP-Universidade Estadual PaulistaBauruBrazil
  4. 4.Instituto de Pesquisas MeteorológicasUNESP-Universidade Estadual PaulistaBauruBrazil

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